Решите систему уравнений: 10-4(2x+5)=6y-13; 4y-63=5(4x-2y)+2.

Ответ:

\[\left\{ \begin{matrix} 10 - 4(2x + 5) = 6y - 13 \\ 4y - 63 = 5(4x - 2y) + 2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 10 - 8x - 20 = 6y - 13\ \ \ \\ 4y - 63 = 20x - 10y + 2 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 8x + 6y = 3\ \ \ \ \ |\ :( - 2)\ \ \ \ \ \\ 20x - 14y = - 65\ \ \ \ \ \ |\ :5 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 4x + 3y = 1,5\ \ \ \ \ \\ - 4x + 2,8y = 13 \\ \end{matrix} \right.\ \ ( + )\]

\[5,8y = 14,5\]

\[y = 14,5\ :5,8 = \frac{145}{58} = \frac{5}{2}\]

\[y = 2,5.\]

\[\left\{ \begin{matrix} y = 2,5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 8x = 3 - 6 \cdot 2,5 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} y = 2,5\ \ \ \ \ \\ 8x = - 12 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} y = 2,5\ \ \ \\ x = - 1,5 \\ \end{matrix} \right.\ \]

\[Ответ:( - 1,5;2,5).\]